Stellar kinematics provides the key to understanding the star formation process. In this respect, we present a kinematic study of the Monoceros OB1 (Mon OB1) and R1 (Mon R1) associations using the recent Gaia data and radial velocities of stars derived from high-resolution spectroscopy and the literature. A total of 728 members are selected using the criteria based on the intrinsic properties of young stars, parallaxes, and proper motions. The spatial distribution and kinematic properties of members show that these associations have distinct substructures. In Mon OB1, we find one northern group and two southern groups. Mon R1 is composed of three small stellar groups that are spatially and kinematically distinct. Some stars are found in a halo around these two associations. We detect patterns of expansion for most stellar groups in the associations. In addition, two stellar groups in Mon OB1 show the signature of rotation, which provides an important constraint on cluster formation. The star formation history of Mon OB1 is slightly revised. Star formation first occurred in the southern region and subsequently in the northern region. Recent star-forming events ignited deeper into the southern region, while some stars are escaping from Mon OB1, forming a halo. Mon R1 might have formed at the same epoch as the formation of the northern group in Mon OB1. Given that star formation is taking place on different scales along a large arc-like structure, Mon OB1 and Mon R1 may be the results of hierarchical star formation.